When Nicolás García Trillos sought a research direction for doctoral studies at Carnegie Mellon University, he was not content simply to trace a straight line a little farther. Instead, he and his adviser identified something new to both of them.
“I didn’t want to feel like I was just following the steps of someone,” said García, a new Prager Assistant Professor of Applied Mathematics. “I wanted to discover something with someone. In this case it was clear that we were going to work together more like side-by-side than top-down. I kind of liked that.”
The problem they tackled was from the field of machine learning, in which algorithms can learn from data. García and his adviser, who had a background in the mathematical field of analysis, had to figure out what tools they should apply to the challenge. Essentially they wanted to ensure that when the algorithms attempt to discern similarities, or clusters, in data, they were consistently doing so in an efficient way.
García now defines his research area as that fusion of analysis, a field that includes calculus and differential equations, and machine learning. What excites him about coming to Brown is the opportunity to again discover something new.
“In a lot of places there would have been more people who share similar work and similar ideas, but I felt that at Brown I could have more things unknown to me, and that I could explore more things,” he said. “I wanted other horizons.”
He arrived in mid-summer and within a few weeks he was already happy to have come.
“It’s been more productive than what I imagined,” he said. “I definitely have the new horizons I was expecting.”
García, a native of Colombia, earned his bachelor’s degree at the Universidad de los Andes in the capital, Bogotá, in 2010. For graduate school he chose Carnegie Mellon. There, he said, he reveled in the diversity of nationalities and academic interests that he encountered.
In his teaching there, which included students from the graduate level to middle school, he found he could enhance his lessons by mixing ideas from different disciplines, just like what he saw at Carnegie Mellon and like he did in his own research.
In particular, to make connecting with math easier for students, he would often enrich the context of the lessons with references to the arts.
“There are a couple of writers that I really like that have explored notions of infinity,” García said. “It’s nice to see how writers can approach these notions.”
In other cases he may use paintings to bring the concepts alive (he credits his wife, an artist, as inspiration for that).
Sometimes it’s just a matter of asking students what else they are studying. In a small undergraduate class on optimization, for example, he learned that his students were simultaneously studying graph theory. So he emphasized the context of graphs in his optimization lessons.
Whether he’s blending analysis with machine learning or the short stories of Jorge Luis Borges with calculus, García seems to always be aiming for new horizons in his work.